Amplifier matrixes such as the well-known Butler matrix have been used in cellular base stations for quite some time. An illustration of a butler matrix used to evenly distribute power amongst three amplifiers 14 is provided in FIG. 1. Typically, a butler matrix has an input matrix portion 12, an output matrix portion 16, amplifiers 14 coupled therebetween, and antennas 18 coupled to the outputs of the output matrix.
Under normal conditions, the amplified outputs of the input portion 12 (i.e., outputs Y1 through Y3) have well-defined mathematical relationships such as, for example,
                    Y        ->            ⁢      1        =                                        1                          3                                ·                      S            ->                          ⁢        1        ⁢        ∠            -              90        ⁢        °            +                                    1                          3                                ·                      S            ->                          ⁢        2        ⁢        ∠0°            +                                    1                          3                                ·                      S            ->                          ⁢        3        ⁢        ∠            -              180        ⁢        °                                Y        ->            ⁢      2        =                                        1                          3                                ·                      S            ->                          ⁢        1        ⁢        ∠60°            +                                    1                          3                                ·                      S            ->                          ⁢        2        ⁢        ∠            -              90        ⁢        °            +                        1                      3                          ⁢                  S          ->                ⁢        3        ⁢        ∠            -              150        ⁢        °                                Y        ->            ⁢      3        =                                        1                          3                                ·                      S            ->                          ⁢        1        ⁢        ∠            -              150        ⁢        °            +                                    1                          3                                ·                      S            ->                          ⁢        2        ⁢        ∠            -              180        ⁢        °            +                                    1                          3                                ·                      S            ->                          ⁢        3        ⁢        ∠            -              120        ⁢        °            
The outputs of the output portion 16 (i.e., outputs Z1 through Z3) have the following mathematical relationships:
                    Z        ->            ⁢      1        =                                        1                          3                                ·                      Y            ->                          ⁢        1        ⁢        ∠            -              150        ⁢        °            +                                    1                          3                                ·                      Y            ->                          ⁢        2        ⁢        ∠60°            +                                    1                          3                                ·                      Y            ->                          ⁢        3        ⁢        ∠            -              90        ⁢        °                                Z        ->            ⁢      2        =                                        1                          3                                ·                      Y            ->                          ⁢        1        ⁢        ∠            -              180        ⁢        °            +                                    1                          3                                ·                      Y            ->                          ⁢        2        ⁢        ∠            -              90        ⁢        °            +                                    1                          3                                ·                      Y            ->                          ⁢        3        ⁢        ∠0°                                Z        ->            ⁢      3        =                                        1                          3                                ·                      Y            ->                          ⁢        1        ⁢        ∠            -              120        ⁢        °            +                                    1                          3                                ·                      Y            ->                          ⁢        2        ⁢        ∠            -              150        ⁢        °            +                                    1                          3                                ·                      Y            ->                          ⁢        3        ⁢        ∠            -              180        ⁢        °            
Applying the Y equations to the Z equations produces the following relationships:
                                                        Z              ->                        ⁢            1                    =                    ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠120°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠                        -                          150              ⁢              °                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠30°                        +                                                                  ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠120°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢                                                          ⁢              2              ⁢              ∠                        -                          30              ⁢              °                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠                        -                          90              ⁢              °                        +                                                                  ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠120°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠90°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠150°                                                                    =                    ⁢                                    S              ->                        ⁢            1            ⁢            ∠120°                                                                                      Z              ->                        ⁢            2                    =                    ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              ∠90°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠180°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠0°                        +                                                                  ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1                        -            ∠30°            +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠180°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠120°                        +                                                                  ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠                        -                          150              ⁢              °                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠180°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠                        -                          120              ⁢              °                                                                    =                    ⁢                                    S              ->                        ⁢            2            ⁢            ∠180°                                                                                      Z              ->                        ⁢            3                    =                    ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠150°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠                        -                          120              ⁢              °                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠60°                        +                                                                  ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠                        -                          90              ⁢              °                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠120°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠60°                        +                                                                  ⁢                                                                      1                  3                                ·                                  S                  ->                                            ⁢              1              ⁢              ∠30°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              2              ⁢              ∠0°                        +                                                            1                  3                                ·                                  S                  ->                                            ⁢              3              ⁢              ∠60°                                                                    =                    ⁢                                    S              ->                        ⁢            3            ⁢            ∠60°                              
These equations reflect a desired isolation characteristic at the outputs of the output portion 16. FIG. 2 shows by way of example reference 20, which depicts the code domain power of a UMTS (Universal Mobile Telecommunications Service) signal at the output portion 16 with all amplifiers operating properly. Under normal operating conditions, for example, the EVM (Error Vector Magnitude) of the UMTS signal of output portion 16 is 5% and peak code domain error is −45.7 dB.
If, however, one of the amplifiers 14 experiences a fault which renders it inoperable, the operation of the Butler matrix can be impacted severely at all outputs of the output portion. This becomes evident in the case where the Y1 amplifier is removed from operation. Under these circumstances, the Z equations result in the following relationships:
                    Z        ->            ⁢      1        =                            2          3                ⁢                  S          ->                ⁢        1        ⁢        ∠120°            +                        1          3                ⁢                  S          ->                ⁢        2        ⁢        ∠30°            +                        1          3                ⁢                  S          ->                ⁢        3        ⁢        ∠            -              150        ⁢        °                                Z        ->            ⁢      2        =                            1          3                ⁢                  S          ->                ⁢        1        ⁢        ∠            -              90        ⁢        °            +                        2          3                ⁢                  S          ->                ⁢        2        ⁢        ∠180°            +                        1          3                ⁢                  S          ->                ⁢        3        ⁢        ∠180°                                Z        ->            ⁢      3        =                            1          3                ⁢                  S          ->                ⁢        ∠            -              30        ⁢        °            +                        1          3                ⁢                  S          ->                ⁢        2        ⁢        ∠60°            +                        2          3                ⁢                  S          ->                ⁢        3        ⁢        ∠60°            
As should be evident from these equations, sector-to-sector isolation degrades severely because of the residual terms between sectors. Consequently, a branch failure within a Butler matrix can cause major degradation in waveform quality at the outputs of the output portion 16. This can cause considerable, if not complete, failure in radio communications to all sectors. FIG. 2 shows by way of example reference 22, which depicts the code domain power of the UMTS signal at the output portion 16 with amplifier Y1 disabled. Under these conditions, the code domain noise has risen 20 dB compared to reference 20, and the EVM and peak code domain error of the UMTS signal of output portion 16 have degraded to 65.5% and −26.5 dB, respectively. A need therefore arises for a fault-tolerant amplifier matrix.